Finite Group Databasebeta

← #11775340

Subgroups — #11775340

Order 1152.

333 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 333 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589702C211yesmaximal, characteristic
2#10588399C211yesmaximal, characteristic, complemented
3#10588330C211yesmaximal, characteristic, complemented
4C9×#327C211yesmaximal, characteristic
5#10588214C211yesmaximal, characteristic
6#10588144C211yesmaximal, characteristic, complemented
7#10588128C211yesmaximal, characteristic, complemented
8#68280—31nomaximal
9C9×#121C2211yescharacteristic
10#63498C411yescharacteristic, complemented
11#63497—21no—
12D4×Dic9—21no—
13D4×Dic9C411yescharacteristic, complemented
14#63486C2211yescharacteristic
15C2×Dic9⋊C4—21no—
16C2×C4×Dic9C2211yescharacteristic
17#63452C411yescharacteristic, complemented
18#63449C411yescharacteristic, complemented
19#63441—21no—
20#63439—21no—
21C9×C22⋊C8C2211yescharacteristic
22C9×#95C2211yescharacteristic
23C9⋊#95—21no—
24C9⋊#95C2211yescharacteristic
25#63389C2211yescharacteristic
26#63375—21no—
27Dic9⋊C8—21no—
28#5600—31no—
29#4719—31no—
30#4650—31no—
31C3×#327D311yescharacteristic
32#4537—31no—
33#4467—31no—
34#4452—31no—
35C2×D4×C9—21no—
36C2×D4×C9C2×C411yescharacteristic
37C22×C4×C9—21no—
38C22×C4×C9C2311yescharacteristic
39C22×Dic9—21no—
40C22×Dic9—21no—
41C22×Dic9D411yescharacteristic
42C22×Dic9D411yescharacteristic
43C2×Dic18C2×C411yescharacteristic
44C2×C8×C9—21no—
45C9×C4⋊C4C2×C411yescharacteristic
46C9×C22⋊C4—21no—
47#3676—21no—
48#3676—21no—
49#3676—21no—
50#3676—21no—
51C4⋊Dic9—21no—
52C4⋊Dic9C2×C411yescharacteristic
53Dic9⋊C4—21no—
54Dic9⋊C4—21no—
55Dic9⋊C4—21no—
56Dic9⋊C4—42no—
57C4×Dic9—21no—
58C4×Dic9C2×C411yescharacteristic
59C4×Dic9C2×C411yescharacteristic
60C4×Dic9D411yescharacteristic
61C4×Dic9D411yescharacteristic
62C2×C9⋊C8—21no—
63#1512—91noSylow
64C3×#121C2×D311yescharacteristic
65#936—31no—
66#935—61no—
67D4×Dic3—31no—
68D4×Dic3—61no—
69#924—31no—
70C2×Dic3⋊C4—61no—
71C2×C4×Dic3—31no—
72#890—31no—
73#887—31no—
74#879—61no—
75#877—61no—
76C3×C22⋊C8C2×D311yescharacteristic
77C3×#95C2×D311yescharacteristic
78C3⋊#95—31no—
79C3⋊#95—61no—
80#830—31no—
81#815—61no—
82Dic3⋊C8—61no—
83C23×C9—21no—
84C23×C9C2×D411yescharacteristic
85D4×C9—41no—
86D4×C9—41no—
87D4×C9—41no—
88C2×C4×C9—21no—
89C2×C4×C9—41no—
90C2×C4×C9—41no—
91C2×C4×C9—41no—
92C2×C4×C9—41no—
93C2×C4×C9C22×C411yescharacteristic
94C2×C4×C9C2×D411yescharacteristic
95C2×Dic9—21no—
96C2×Dic9—21no—
97C2×Dic9—21no—
98C2×Dic9—21no—
99C2×Dic9—41no—
100C2×Dic9—42no—
101C2×Dic9—41no—
102C2×Dic9—41no—
103C2×Dic9—41no—
104C2×Dic9C22⋊C411yescharacteristic
105C2×Dic9C22⋊C411yescharacteristic
106C2×Dic9C22⋊C411yescharacteristic
107C2×Dic9C22⋊C411yescharacteristic
108Dic18—41no—
109C8×C9—41no—
110C9⋊C8—41no—
111#529—91no—
112#432—91no—
113#382—91no—
114#328—91no—
115#328—91no—
116#327—91no—
117#327D911yescharacteristic
118C2×C3×D4—21no—
119C2×C3×D4C4×D311yescharacteristic
120C22×C3×C4—21no—
121C22×C3×C4C22×D311yescharacteristic
122C22×Dic3—31no—
123C22×Dic3—31no—
124C22×Dic3—61no—
125C22×Dic3—61no—
126C2×Dic6—31no—
127C2×C3×C8—21no—
128C3×C4⋊C4C4×D311yescharacteristic
129C3×C22⋊C4—21no—
130#217—61no—
131#217—61no—
132#217—61no—
133#217—61no—
134C4⋊Dic3—31no—
135C4⋊Dic3—61no—
136Dic3⋊C4—61no—
137Dic3⋊C4—61no—
138Dic3⋊C4—61no—
139Dic3⋊C4—122no—
140C4×Dic3—31no—
141C4×Dic3—31no—
142C4×Dic3—31no—
143C4×Dic3—31no—
144C4×Dic3—61no—
145C2×C3⋊C8—61no—
146C22×C9—21no—
147C22×C9—21no—
148C22×C9—41no—
149C22×C9—41no—
150C22×C9—41no—
151C22×C9C2×C22⋊C411yescharacteristic
152C22×C9AGL(1,ℤ/8)11yescharacteristic
153C22×C9#13711yescharacteristic
154C4×C9—21no—
155C4×C9—21no—
156C4×C9—41no—
157C4×C9—81no—
158Dic9—21no—
159Dic9—21no—
160Dic9—21no—
161Dic9—21no—
162Dic9—41no—
163Dic9—41no—
164Dic9—81no—
165#126—181no—
166#125—91no—
167#124—91no—
168#123—181no—
169C22⋊Q8—91no—
170#121C2×D911yescharacteristic
171C4×Q8—91no—
172C4×D4—91no—
173C4×D4—181no—
174#117—181no—
175C2×C4⋊C4—181no—
176C2×C42—91no—
177C4⋊C8—181no—
178C22⋊C8—91no—
179C22⋊C8C2×D911yescharacteristic
180#97—181no—
181#95—91no—
182#95—181no—
183#95C2×D911yescharacteristic
184C23×C3—21no—
185C23×C3D3×D411yescharacteristic
186C3×D4—41no—
187C3×D4—41no—
188C3×D4—41no—
189C2×C3×C4—21no—
190C2×C3×C4—41no—
191C2×C3×C4—41no—
192C2×C3×C4—41no—
193C2×C3×C4—41no—
194C2×C3×C4C2×C4×D311yescharacteristic
195C2×C3×C4D3×D411yescharacteristic
196C2×Dic3—31no—
197C2×Dic3—31no—
198C2×Dic3—31no—
199C2×Dic3—31no—
200C2×Dic3—61no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—121no—
205C2×Dic3—122no—
206C2×Dic3—121no—
207C2×Dic3—121no—
208C2×Dic3—121no—
209Dic6—121no—
210C3×C8—41no—
211C3⋊C8—121no—
212C2×C9—21no—
213C2×C9—21no—
214C2×C9—81no—
215C2×C9#41011yescharacteristic
216C2×C9#41711yescharacteristic
217C2×C9#42111yescharacteristic
218C2×Q8—91no—
219C2×D4—21no—
220C2×D4C4×D911yescharacteristic
221C22×C4—21no—
222C22×C4—91no—
223C22×C4—91no—
224C22×C4—181no—
225C22×C4—181no—
226C22×C4C22×D911yescharacteristic
227C2×C8—21no—
228C2×C8—181no—
229C4⋊C4—91no—
230C4⋊C4—181no—
231C4⋊C4—181no—
232C4⋊C4—181no—
233C4⋊C4—181no—
234C4⋊C4—362no—
235C4⋊C4C4×D911yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—181no—
238C22⋊C4—181no—
239C22⋊C4—181no—
240C22⋊C4—181no—
241C42—91no—
242C42—91no—
243C42—91no—
244C42—91no—
245C42—181no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—41no—
249C22×C3—41no—
250C22×C3—41no—
251C22×C3D3×C22⋊C411yescharacteristic
252C22×C3#91111yescharacteristic
253C22×C3#91511yescharacteristic
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—41no—
257C3×C4—81no—
258Dic3—61no—
259Dic3—61no—
260Dic3—61no—
261Dic3—61no—
262Dic3—121no—
263Dic3—121no—
264Dic3—241no—
265C9#151211yescharacteristic, complemented, Sylow
266C23—21no—
267C23D4×D911yescharacteristic
268Q8—361no—
269D4—41no—
270D4—41no—
271D4—41no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—91no—
278C2×C4—91no—
279C2×C4—91no—
280C2×C4—91no—
281C2×C4—181no—
282C2×C4—181no—
283C2×C4—181no—
284C2×C4—181no—
285C2×C4—361no—
286C2×C4—362no—
287C2×C4—361no—
288C2×C4—361no—
289C2×C4—361no—
290C2×C4C2×C4×D911yescharacteristic
291C2×C4D4×D911yescharacteristic
292C8—41no—
293C8—361no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—81no—
297C2×C3#474011yescharacteristic
298C2×C3#477111yescharacteristic
299C2×C3#482111yescharacteristic
300C22—21no—
301C22—21no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22C22⋊C4×D911yescharacteristic
306C22#6347311yescharacteristic
307C22#6347711yescharacteristic
308C4—21no—
309C4—21no—
310C4—41no—
311C4—81no—
312C4—181no—
313C4—181no—
314C4—181no—
315C4—181no—
316C4—361no—
317C4—361no—
318C4—721no—
319C3#6828011yescharacteristic
320C2—21no—
321C2—21no—
322C2—81no—
323C2#1058842011yescharacteristic
324C2#1058845111yescharacteristic
325C2#1058850111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D9
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#327C2
socleC22×C3D3×C22⋊C4
prime radicalC3×#121C2×D3
cosocleC22×C4×C9C23
hypercenter#327D9
hypocenterC9#1512
LCSG ▷ C2×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10588399C2semidirect
3. #10588330C2semidirect
6. #10588144C2semidirect
7. #10588128C2semidirect
10. #63498C4semidirect
13. D4×Dic9C4semidirect
17. #63452C4semidirect
18. #63449C4semidirect
265. C9#1512semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105897022
#105883992
#105883302
C9×#3272
#105882142
#105881442
#105881282
#682803